Minimization Problems Based on Relative <inline-formula>  src='/images/tex/25750.gif' alt='alpha '> </inline-formula>-Entropy II: Reverse Projection

Ashok Kumar M.; Sundaresan Rajesh

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Minimization Problems Based on Relative src='/images/tex/25750.gif' alt='alpha '> -Entropy II: Reverse Projection

机译：基于相对 src =“ / images / tex / 25750.gif” alt =“ alpha”> -熵II：反投影

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摘要

In part I of this two-part work, certain minimization problems based on a parametric family of relative entropies (denoted ) were studied. Such minimizers were called forward -projections. Here, a complementary class of minimization problems leading to the so-called reverse -projections are studied. Reverse -projections, particularly on log-convex or power-law families, are of interest in robust estimation problems () and in constrained compression settings (). Orthogonality of the power-law family with an associated linear family is first established and is then exploited to turn a reverse -projection into a forward -projection. The transformed problem is a simpler quasi-convex minimization subject to linear constraints.

机译：在这个由两部分组成的工作的第一部分中，研究了基于相对熵（表示为）的参数族的某些最小化问题。这种最小化器称为前向投影。在这里，研究了导致所谓的反向投影的最小化问题的补充类。反投影，尤其是在对数凸或幂律族上，对鲁棒估计问题（）和受约束的压缩设置（）感兴趣。首先建立幂律族与相关联的线性族的正交性，然后利用正交性将反投影变为正投影。变换后的问题是受线性约束的更简单的准凸极小化。

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来源
《Information Theory, IEEE Transactions on》 |2015年第9期|5081-5095|共15页
作者
Ashok Kumar M.; Sundaresan Rajesh;
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作者单位

Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa, Israel;

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正文语种 eng
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关键词
Best approximant; Kullback-Leibler divergence; Pythagorean property; R??nyi entropy; Renyi entropy; Tsallis entropy; exponential family; information geometry; linear family; power-law family; projection; relative entropy; robust estimation;

机译：最佳近似;Kullback-Leibler散度;勾股定律;R ?? nyi熵;Renyi熵;Tsallis熵;指数族;信息几何;线性族;幂律族;投影;相对熵;鲁棒估计;

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1. Minimization Problems Based on Relative src="/images/tex/25750.gif" alt="alpha "> -Entropy I: Forward Projection [J] . Kumar M. Ashok, Sundaresan Rajesh Information Theory, IEEE Transactions on . 2015,第9期

机译：基于相对 src =“ / images / tex / 25750.gif” alt =“ alpha”> -熵I：正投影
2. Magnetic Determination of the Electronic State of Cu and Exchange Interactions in the src="/images/tex/25750.gif" alt="alpha "> - and src="/images/tex/25935.gif" alt="beta "> -Phases of Molecular Semiconductor Copper Phthalocyanine (C₃₂H₁₆N₈Cu) [J] . Wang Zhengjun, Pisane Kelly L., Seehra Mohindar S. Magnetics, IEEE Transactions on . 2015,第11期

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3. src="/images/tex/28744.gif" alt="NP/CMP"> Equivalence: A Phenomenon Hidden Among Sparsity Models src="/images/tex/27950.gif" alt="l_{0}"> Minimization and src="/images/tex/25757.gif" alt="l_{p}"> Minimization for Information Processing [J] . Peng Jigen, Yue Shigang, Li Haiyang Information Theory, IEEE Transactions on . 2015,第7期

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4. The ENDECO® DATA-WATCH ADAPTIVE src="/images/tex/225.gif" alt="^{TM}"> Packet Telemetry System [C] . Mernyk R. Oceans '87 proceedings . 1987

机译：ENDECO®数据手表自适应 src =“ / images / tex / 225.gif” alt =“ ^ {TM}”>分组遥测系统
5. Calibration of Linear Time-Varying Frequency Errors for Distributed ISAR Imaging Based on the Entropy Minimization Principle [O] . Hailong Kang, Jun Li, Hongyan Zhao, 2019

机译：基于熵最小化原理的分布式ISAR成像线性时变频率误差标定
6. Minimization Problems Based on Relative alpha-Entropy II: Reverse Projection [O] . Kumar, Ashok M, Sundaresan, Rajesh 2015

机译：基于相对α熵的最小化问题II：反投影
7. Relative Entropy-Based Approach to Image Thresholding; Journal article [R] . Chang, C., Chen, K., Wang, J., 1994

机译：基于相对熵的图像阈值处理方法;杂志文章

Minimization Problems Based on Relative src='/images/tex/25750.gif' alt='alpha '> -Entropy II: Reverse Projection

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